Cyclone Hudhud is pounding the eastern Indian coast, causing extensive damage and prompting the evacuation of some 350,000 people.
At least three people have been killed in Andhra Pradesh and three in Orissa.
The cyclone, classed "very severe", brought winds of 205km/h (127mph), as it passed over the coast near the city of Visakhapatnam.
The winds and heavy rains have brought down trees and power lines, and damaged crops and buildings in both states.
It is feared a storm surge of up to two metres could inundate low-lying areas and hundreds of relief centres have been opened in the two states. Disaster relief teams have also been sent.
Andhra Pradesh Chief Minister Chandrababa Naidu said it was too early to assess the damage fully.
"We are unable to ascertain the situation; 70% of communication has totally collapsed," he said.
"We are asking people not to come out of their houses. We are mobilising men and materiel immediately."
The three deaths in Andhra Pradesh occurred in separate incidents in Visakhapatnam and Srikakulam districts, Chief Secretary IYR Krishna Rao said.
Two were killed by falling trees and one by a collapsing wall.
Anil Shekhawat, from the National Disaster Response Force (NDRF), told the BBC: "The cyclone has landed... The NDRF is there - we have sent around 42 teams, comprising more than 2,000 rescuers."
The streets of Visakhapatnam, one of the largest cities in south-east India and home to a major naval base, remain largely deserted.
N Yuvaraj, a senior district official in Visakhapatnam, told the BBC: "We had this cyclone hitting us at around 10:25 Indian Standard Time (04:55 GMT). And at that point we had a wind speed of more than 205km/h."
K Hymavathi, the special commissioner for disaster management for Andhra Pradesh state, said: "Hundreds of trees have been uprooted and power lines knocked down."
He added: "The situation is very severe. The national highway in the region has been shut."
Local journalist Hridayesh Joshi told the BBC from Visakhapatnam: "The situation is becoming increasingly bad. There is very strong wind and rain right now - objects are flying and smashing things.
"We are relatively safe in the centre of town, but the danger is for those in open areas. We are hoping it won't get much worse."
In its latest report, the India Meteorological Department said sea conditions would become "phenomenal" off the north Andhra Pradesh and south Orissa coasts.
It also warned that a storm surge of up to two metres would "inundate low-lying areas of Visakhapatnam, Vijayanagaram and Srikakulam".
The director of the Bhubaneswar centre of the IMD, Sarat Sahu, told the BBC that Hudhud was "likely to trigger heavy rains in most parts of south Orissa and the neighbouring states of Chhattisgarh and Telengana", raising fears of heavy flooding.
India's eastern coast and Bangladesh are routinely hit by cyclonic storms between April and November which cause deaths and widespread damage to property.
A super-cyclone in 1999 killed more than 10,000 people in Orissa.
Last October as many as 500,000 people in India were evacuated when a severe cyclone called Phailin swept through Orissa and Andhra Pradesh states.